Robust hyperplane fitting based on k-th power deviation and α-quantile

Jun Fujiki, Shotaro Akaho, Hideitsu Hino, Noboru Murata

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

In this paper, two methods for one-dimensional reduction of data by hyperplane fitting are proposed. One is least α-percentile of squares, which is an extension of least median of squares estimation and minimizes the α-percentile of squared Euclidean distance. The other is least k-th power deviation, which is an extension of least squares estimation and minimizes the k-th power deviation of squared Euclidean distance. Especially, for least k-th power deviation of 0 < k ≤ 1, it is proved that a useful property, called optimal sampling property, holds in one-dimensional reduction of data by hyperplane fitting. The optimal sampling property is that the global optimum for affine hyperplane fitting passes through N data points when an N-1-dimensional hyperplane is fitted to the N-dimensional data. The performance of the proposed methods is evaluated by line fitting to artificial data and a real image.

本文言語English
ホスト出版物のタイトルComputer Analysis of Images and Patterns - 14th International Conference, CAIP 2011, Proceedings
編集者Pedro Real, Daniel Diaz-Pernil, Helena Molina-Abril, Ainhoa Berciano, Walter Kropatsch
出版社Springer Verlag
ページ278-285
ページ数8
ISBN(印刷版)9783642236716
DOI
出版ステータスPublished - 2011
イベント14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011 - Seville, Spain
継続期間: 2011 8 292011 8 31

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
6854 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Conference

Conference14th International Conference on Computer Analysis of Images and Patterns, CAIP 2011
国/地域Spain
CitySeville
Period11/8/2911/8/31

ASJC Scopus subject areas

  • コンピュータ サイエンス(全般)
  • 理論的コンピュータサイエンス

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